Missing data: the wave number

(a) 
For a transverse wave travelling in the positive y-direction and with vibration along the z-direction, the equation of the wave is

where
A is the amplitude of the wave
k is the wave number
is the angular frequency
t is the time
In this situation:
A = 3.0 mm = 0.003 m is the amplitude
is the wave number
is the period, so the angular frequency is

So, the wave equation (in meters) is

(b) 0.094 m/s
For a transverse wave, the transverse speed is equal to the derivative of the displacement of the wave, so in this case:

So the maximum transverse wave occurs when the cosine term is equal to 1, therefore the maximum transverse speed must be

where

Substituting,

(c) 5.24 mm/s
The wave speed is given by

where
f is the frequency of the wave
is the wavelength
The frequency can be found from the angular frequency:

While the wavelength can be found from the wave number:

Therefore, the wave speed is
